A student of mine was told by a native German that they do not say
Ich habe Hunger.
Ich bin hungrig.
Is the first expression outdated?
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Ich habe Hunger is perfectly acceptable on all levels of conversation and used without afterthought as a viable alternative to Ich bin hungrig. The former is neither outdated, nor inappropriate in any way.
This is based on the experience of a German native to eastern Germany.
Using Google nGrams, it appears that Ich habe Hunger is in fact more commonly used than the alternative, having significantly increased in relative popularity since the 1970s.
As already told both expressions are used. However, there's a difference. »Ich habe Hunger« always refers to food, »Ich bin hungrig« not necessarily, it can mean »I'm ambitious«.
A person also can be
hungrig nach Liebe / Anerkennung / Abenteuern ...
(hungry for love / acceptance / adventures ...)